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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 4

On the tensor-product Hilbert space, <addition of angular momentum> gives
$$
\mathbf J=\mathbf J_1\otimes I_2+I_1\otimes\mathbf J_2.
$$
Suppressing the identity operators, its components and <spin ladder operator>[ladder operators] are
$$
J_x=J_{1x}+J_{2x},
\quad
J_y=J_{1y}+J_{2y},
\quad
J_z=J_{1z}+J_{2z},
$$
$$
J_\pm=J_x\pm iJ_y=J_{1\pm}+J_{2\pm}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 33B / a / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 33B / a / i / Solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 33B / a / i / Solution

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